When i write a sentence then do i have a copyright upon it which i can defend in law? No. Yes copyright is nothing you get, that in theory is correct but in practice a sentence or few lines of code don't let me fight for them in court.
The current models are all trained with data which at least some larger creator (book writer or whatever) does not want a model to be trained on. So the discussion is a complete other, not how ppl will be compensated on their unlawful use of their data but on how the payment works in the future and here comes my first comment back.
The current models are under the current law unsustainable. And more and more courts rule in this direction.